(adsbygoogle = window.adsbygoogle || []).push({}); HELP: A summation question

Hi

Given the sum

[tex]\sum _{p=0} ^{\infty} (-1)^p \frac{4p+1}{4^p}[/tex]

I have tried something please tell if I'm on the right track

Looking at the alternating series test

(a) [tex]1/(4^{p+1}) < (1/(4^p))[/tex]

(b) [tex]\mathop {\lim }\limits_{p \to \infty } b_p = \mathop {\lim }\limits_{p \to \infty } \frac{1}{{4^p }} = 0[/tex]

Then according to the test this allows me to write [tex]\sum _{p = 0} ^{\infty} 4^{-p} = 4/3[/tex]

Can anybody please verify if I'm heading in the right direction on this? Or am I totally wrong?

Sincerely Yours

Hummingbird

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# Homework Help: A summation question

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